Problem: $ E = \left[\begin{array}{rr}4 & 1\end{array}\right]$ $ F = \left[\begin{array}{rrr}4 & -2 & -1\end{array}\right]$ Is $ E+ F$ defined?
Answer: In order for addition of two matrices to be defined, the matrices must have the same dimensions. If $ E$ is of dimension $( m \times  n)$ and $ F$ is of dimension $( p \times  q)$ , then for their sum to be defined: 1. $ m$ (number of rows in $ E$ ) must equal $ p$ (number of rows in $ F$ ) and 2. $ n$ (number of columns in $ E$ ) must equal $ q$ (number of columns in $ F$ Do $ E$ and $ F$ have the same number of rows? Yes Yes No Yes Do $ E$ and $ F$ have the same number of columns? No Yes No No Since $ E$ has different dimensions $(1\times2)$ from $ F$ $(1\times3)$, $ E+ F$ is not defined.